1 / 45

SCITT Day 4 2018

Study the NC2014 approach to multiplication and division, develop fluency of times tables, and explore different representations and written methods. Consider the role of calculators and links to measurement.

josedaniels
Télécharger la présentation

SCITT Day 4 2018

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. SCITT Day 4 2018 Multiplication (and links to Division)

  2. Representing numbers 66

  3. DAY 2 - Talk through each example..

  4. DAY 4 - CALCULATION – MULTIPLICATION with some links to division • Study the NC2014 approach to multiplication and division including using manipulatives and/or recording mental methods, informal jottings and formal written methods; • Consider how the use and complexity of arrays progress through the primary years • Explore the importance of developing fluency of times tables and deriving related division facts Associated Issues for Teaching • The role of calculators in the classroom • Making links to Measurement • Multiplication – facts, representations, flexible, connections, grid, formal • Division – making connections

  5. Reading for Day 4

  6. My role: Provide time to think and consider You: Make sense of the ideas and activities Stop and ask questions…

  7. Words/ phrases x and ÷ What different words/ phrases can you list… ?

  8. Day 4 - Multiplication and Division Multiplication as repeated addition Arrays  grid method Standard written methods Arrays Multiplication as scaling Build it Language Models and images White Rose Calculation guidance Understanding x/÷ Fluency Learning x tables Division as grouping Division as sharing Links between x/÷ Understandings and connections  Number facts  Written methods

  9. Representations… “4 children each have a bag of sweets, there are 3 sweets in each bag.” • Represent MANY ways [&…? &…?] • Unstructured v structured • Language/ vocabulary Cubes Counters Tens Frames Numicon Number rods Dienes …….. Number lines X grids Other…? “Show me. Convince me.” Cbuild it, make it Pdraw or sketch it Avisualise, write it • Key Messages: • Identifying a group • Orientation • Making connections • Commutativity • Division • Representation matching language!

  10. Two types of multiplication • Repeated addition • Scaling Tracking National Curriculum Expectations • What are the expectations for x and ÷ in your year group? • Are both multiplication types mentioned? • Any ‘unclear’ language/ any examples required? 2 2 + 2 + 2 2 2 2 ‘3 times longer’

  11. WRMH guidance • Make sense of the images • Are there important messages? • Compare with practice in your classroom What other CPA images could you add to this guidance?

  12. 3 x 5 = How could you work it out? 2 x sentences 2 ÷ sentences

  13. Secrets for Cheating at x tables Secret 1: If you know one fact, then you know a second. Secret 2 X tables always give you a buy one, get three free offer. Secret 3: If you can double, then you can multiply by 2, 4 and 8. Secret 4: If you can multiply by 1, then you can multiply by 10. Secret 5: If you can halve, then you can multiply by 5. Secret 6: If you use fingers, then you can multiply by 9 Nines in your head: Multiply by 10 and then adjust Secret 7: If you know the 3 times table, then you know the 6 times table.

  14. If I know that 5 x 7 = 35 Repeated addition Place Value 50 x 7 = 500 x 7 = 0.5 x 7 = 5 + 5 + 5 + 5 + 5 + 5 + 5= 7 + 7 + 7 + 7 + 7 = Any order and inverse 7 x 5 = 35 35 ÷ 7 = 5 35 ÷ 5 = 7 Fractions One fifth of 35 = 7 Two fifths… Three fifths… One seventh of 35 = 5 Two sevenths… 6 x 7 = Or 4 x 7 = Derive new facts from known facts Repeated subtraction 5 x 6 = Or 5 x 8 = 35 – 7 – 7 – 7 – 7 – 7 = 0 35 – 5 – 5 – 5 – 5 – 5 – 5 – 5 = 0

  15. H T U? 0 2 4 0

  16. Making your own ‘fact families’ x and ÷ cards 3 x 4 =12 4 x 3=12 12÷3=4 12 shared between 3 equals 4 One third of 12 = 4 ¼ of 12 = 3

  17. Formal methods… 1st Learners UNDERSTAND what x/÷ is 2nd x/÷ facts are fluent 3rd Learners apply their learning to solve problems Then ready to explore a progression to formal methods

  18. ‘Grid’ or ‘Area’ multiplication Multiplication 13 x 6 = 3 10 60 18 60 + 18 = 78 6 Can this be built more efficiently? so 13 x 6 = 78

  19. Multiplication 13 x 6 = NB from reading 78 ÷ 6 = (60 + 18) ÷ 6 = 10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 Now build and record: 24 x 3 = 125 x 4 =

  20. Just use grid multiplication… 64 x 8 = 234 x 6 = 34 x 78 =

  21. 2100 280 = 2380 240 32 = 272 Grid method 3 4 7 8 x 3 2 2 4 0 2 8 0 2 1 0 0 + 2 6 5 2 3 4 8 x 2 7 2 3 4 7 8 x 2 7 2 2 3 8 0+ 2 6 5 2 2 3 8 x 4 8 x 30 70 x 4 70 x 30 3 4 7 0 x 2 3 8 0 1 1 Long multiplication Expanded method 2 x Short multiplication

  22. White Rose Materialswww.whiterosemaths.com Planning Task: Time to explore the materials and engage with the mathematics activities and ideas… What are the age-related expectations? What ideas are offered to cement fluency? How do the R &PS activities offer challenge? (Through breadth…? depth…?) OTHER SLIDES FOLLOW…

  23. To find all Blocks/ Units on TESwww.whiterosemaths.com

  24. Two structures of division • Sharing (links with ‘finding fractions of amounts’) • Grouping (repeated subtraction) Draw a picture… • There are 18 sweets share equally between 3… • There are 18 sweets, divide them into 3s… Other models and images…? Counters/ arrays/ number lines/ number rods/ Numicon …

  25. The language of division Should always use the language ‘divided’ 18 ÷ 3 = “18 dividedby 3” Sharing – “18 dividedbetween 3” Grouping – “18 divided into 3’s” How would you calculate 18 ÷ 3 = ? Also a fraction: “Each equal part is a third” Language must match the model

  26. Division 18 ÷ 3 = 18 grouped into 3’s How many 3’s in 18? 18 shared equally between 3 How many each? “One for you, one for you…” Answer 6 6 each 6 groups

  27. Division 18 ÷ 3 = 18 grouped into 3’s How many 3’s in 18? What would this look like with Numicon? With Number rods? Answer 6 Equal in area Equal in length

  28. Remainders 20 ÷ 3 = 6 r2 20 grouped into 3’s How many 3’s in 20? 20 shared equally between 3 “One for you, one for you…” ‘Remainder 2’ or 2 ‘left over’ 2 2

  29. Calculate… 21 ÷ 3 = 24 ÷ 6 = 15 ÷ 5 = 20 ÷ 4 = 24 ÷ 8 = 35 ÷ 7 = Remainders 26 ÷ 5 = 25 ÷ 4 = Going over ‘10x’ - mental 38 ÷ 2 = 39 ÷ 3 = 44 ÷ 4 = 48 ÷ 6 = Calculate then discuss ‘how to teach’ • Numicon • Number rods • Counters/ cubes  arrays • Dienes

  30. Splitting 81 ÷ 3 = Moving beyond the 10x table… How can I split this number using knowledge of the 3 x table? Do it Sharing or grouping? 10 1 10 10 10 10 10 10 10

  31. Splitting 81 ÷ 3 = Moving beyond the 10x table… How can I split this number using knowledge of the 3 x table? This could be sharing between 3 people (horizontal) “10 for you, 10 for you…” OR as a group/ column of 3 tens Do it 1 10 10 10 10 10 10 10 10

  32. Splitting 81 ÷ 3 = How can I split this number using knowledge of the 3 x table? 3 X ? ? ? 30 30 21 10 + 10 + 7 = 27 Practice: 84 ÷ 7 = / 72 ÷ 3 = / 65 ÷ 5 =

  33. Division – Written MethodsWhat happens when the dividend goes beyond 10 x ? Use sharing or grouping to build an array for: 10 1 10 1 52 ÷ 4 = 10 10 10

  34. Division – Written Methods with Base 10 52 ÷ 4 = 3 1 1 1 Grouping in 4s – REMOVING THE PLACE VALUE “How many groups of 4 (in each column)?”

  35. Division – Written Methods with Base 10 52 ÷ 4 = 1 1 10 1 C build it, make it P draw or sketch it A visualise, write it 1 1 1 10 1 1 1 10 1 1 1 10 Making links back to grid method

  36. Division – Written Methods with Base 10 72 ÷ 3 = 10 10 10 10 1 1 C build it, make it P draw or sketch it A visualise, write it 10 10 10 Making links back to grid method

  37. 94 ÷ 4 = 94 ÷ 4 = 2 3 r2 Chunking Short Division 4 9 4 9 4 4 0 – 5 4 4 0 – 1 4 1 2 – 2 10 x 10 x 3 x 23 r2 1 How many groups of 4 are in this column? 2 r1 How many groups of 4 are in this column? 3 r2 )

  38. 98 ÷ 7 = Long division How many 7s in this column? Short division 98 - 70 28 - 28 0 10x 4 x 1 4 2 How many 7s in this column?

  39. Your turn! Use chunking & short division to work out 144 ÷ 6 =

  40. Designing learning for short division NCETM

  41. Mathematics Appendix

  42. TASK 2a and 2b[EITHER +/- or x/ ÷] HAND IN DAY 5 • TASK 2b: Observe a lesson where a model/ image is used by the teacher and/or learners. After the lesson interview the children and critically evaluate the impact on their understanding. • LEARNING OUTCOME: To be more aware of the important role of models and images when teaching for mastery understanding • Maths TASK 2a – Briefly review the use models and images used in your classroom (CPA) for Place Value. Photo/ sketch/ draw the models to discuss how they are used. • LEARNING OUTCOME: To be more aware of the important role of models and images when teaching for understanding

  43. GROUP READING FOR DAY 5: • D Haylock ‘Mathematics Explained for Primary Teachers’ Third Edition • Chapter 14 ‘Fractions and Ratios’

More Related